How is a determinant found using expansion by minors?

Question

The only way I was taught to do it was by using diagonals.

Answer 1

check this page

http://mathworld.wolfram.com/DeterminantExpansionbyMinors.html

It is presented better than we could do on this format

Answer 2

upper left * det of the rest without that row and column
- second down on left times det of everything without that row and column
+ third down on left times det of everything without that row and column

etc down that left column alternating signs until you get to the bottom left.

Answer 3

In the trivial case of
a b
c d
it would be
a (d)
-c(b)
which you knew already

Answer 4

thanks

Answer 5

now for the slightly less trivial
a b c
d e f
g h i

a times det
e f
h i

- d times det
b c
h i

+ g times det
b c
e f

which is
a (e i - h f)
-d(b i - h c)
+g(b f - e c )
which is
a e i - a h f - d b i + d h c + g b f - g e c
which is the same as you get using the diagonal method